Best Weighting Scheme for a Stock Portfolio?

What is the overall best way to weight stock portfolios? In their February 2022 paper entitled “Weighting for the Right One: Weighting Scheme Design for Systematic Equity Portfolios”, Wei Dai, Namiko Saito and Gigi Wang compare eight stock portfolio weighting schemes frequently used in systematic strategies, five that ignore prices and three that do not, as follows:

• Weighting schemes that ignore prices are:
  1. Equal weighting – assign all stocks the same dollar weight.
  2. Rank weighting – separately rank all stocks from large to small, growth to value and low to high profitability, and then re-rank and weight based on averages of individual ranks.
  3. Z-score weighting: separately calculate z-scores (number of standard deviations from average) for each firm’s market capitalization, relative price and profitability, transform the z-scores into a value between 0 and 1, and weight in proportion to the product of the three standardized z-scores.
  4. Inverse volatility weighting: weight each stock in proportion to the inverse of its daily return volatility over the last 60 trading days.
  5. Fundamental weighting: weight each stock in proportion to the sum of book equity, sales and cash flow per share during its latest fiscal year.
• Weighting schemes that incorporate prices are:
  1. Rank x mcap: weight each stock in proportion to the product of its rank weighting (as defined above) and its market capitalization.
  2. Z-score x mcap: weight each stock in proportion to the product of its standardized z-scores (as defined above) and its market capitalization.
  3. Integrated core: separately sort all firms by market capitalization, relative price and profitability into groups with similar characteristics; within each group, weight firms in proportion to their market capitalizations; and, further weight each group in proportion to its aggregate market capitalization times a multiplier capturing its overall size, value and profitability premiums as modified for interactions among them.

They rebalance each portfolio semiannually. They consider stock universes with and without microcaps (bottom 4% of market capitalizations). Their approach focuses on the importance of accounting for current market prices that reflect the latest news and market expectations. Using data as described for all U.S. common stocks (excluding REITs, tracking stocks and investment companies) during July 1974 through December 2019, they find that:

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